In various animal species individuals differ consistently in their behaviour, often referred to as personality. In several species these personality differences also correlate with differences in social behaviour. This is important as the social environment is a key selection pressure in many animal populations, mediated, for example, via competition or access to social information. Using social network analysis, recent studies have furthered our understanding of the role of personality in the social environment, usually by focusing on swarming or flocking populations. However, social associations in such populations are fundamentally different from those in territorial populations, where individuals meet less frequently and where the costs and benefits of spatial associations differ from those for swarming or flocking species. In this study we therefore tested whether social network position is related to individual differences in exploration behaviour, an established measure of an avian personality trait, using a wild, territorial, personality-typed great tit, Parus major, population. By means of novel, large-scale, automated tracking (Encounternet) we show, while controlling for average territory distance, that slower exploring males had less central social network positions. Yet, slower explorers overall did not travel shorter distances than faster explorers, indicating that a less central social network position was not merely a consequence of lower activity. Finally, males with less central social network positions did not have reduced breeding success compared to males with more central positions. Our results suggest that territorial individuals influence the structuring of their own social environment in relation to their personality. This is relevant, because the establishment of social relations and familiarity with possible competitors is predicted to be important in many territorial populations.